Novel Stable Approach with Probability Distribution for Multi-Criteria Decision-Making Problems of Multi-Valued Neutrosophic Sets

2020 ◽  
Vol 19 (05) ◽  
pp. 1271-1292
Author(s):  
Xu Libo ◽  
Li Xingsen ◽  
Cui Honglei
Keyword(s):  
Decision Making ◽  
Probability Distribution ◽  
Dynamic Change ◽  
Distribution Functions ◽  
Transformation Operator ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Dependent Function ◽  
Novel Approach

In this paper, a novel approach and framework based on interval-dependent degree and probability distribution for multi-criteria decision-making problems with multi-valued neutrosophic sets (MVNSs) is proposed. First, a simplified dependent function and distribution function are given and integrated into a concise formula, which is called the interval-dependent function and contains interval computing and probability distribution information in an interval. Then a transformation operator is defined and it is shown how to convert MVNSs into an interval set. Subsequently, the interval-dependent function with the probability distribution of MVNSs is deduced. Finally, an example and comparative analysis are provided to verify the feasibility and effectiveness of the proposed method. In addition, uncertainty analysis, which reflects the dynamic change of the ranking result with decision-makers’ preferences, is performed by setting different distribution functions, which increases the reliability and accuracy of the proposed method.

scholarly journals Simplified Neutrosophic Sets Based on Interval Dependent Degree for Multi-Criteria Group Decision-Making Problems

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 640 ◽  
Author(s):  
Xu Libo ◽  
Li Xingsen ◽  
Pang Chaoyi ◽  
Guo Yan
Keyword(s):  
Decision Making ◽  
Distribution Function ◽  
Group Decision Making ◽  
Group Decision ◽  
Dynamic Change ◽  
Transformation Operator ◽  
Decision Makers ◽  
Neutrosophic Sets ◽  
New Approach ◽  
Dependent Function

In this paper, a new approach and framework based on the interval dependent degree for multi-criteria group decision-making (MCGDM) problems with simplified neutrosophic sets (SNSs) is proposed. Firstly, the simplified dependent function and distribution function are defined. Then, they are integrated into the interval dependent function which contains interval computing and distribution information of the intervals. Subsequently, the interval transformation operator is defined to convert simplified neutrosophic numbers (SNNs) into intervals, and then the interval dependent function for SNNs is deduced. Finally, an example is provided to verify the feasibility and effectiveness of the proposed method, together with its comparative analysis. In addition, uncertainty analysis, which can reflect the dynamic change of the final result caused by changes in the decision makers’ preferences, is performed in different distribution function situations. That increases the reliability and accuracy of the result.

scholarly journals Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1081 ◽  
Author(s):  
Peng ◽  
Tian ◽  
Zhang ◽  
Song ◽  
Wang
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Preference Information ◽  
Fuzzy Measures ◽  
Correlative Relationship

Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.

scholarly journals A Novel Dynamic Multi-Criteria Decision Making Method Based on Generalized Dynamic Interval-Valued Neutrosophic Set

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 618 ◽  
Author(s):  
Nguyen Tho Thong ◽  
Florentin Smarandache ◽  
Nguyen Dinh Hoa ◽  
Le Hoang Son ◽  
Luong Thi Hong Lan ◽  
...  
Keyword(s):  
Decision Making ◽  
Evaluation Model ◽  
Real Life ◽  
Decision Makers ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Proposed Model ◽  
Interval Valued ◽  
Knowledge Evaluation

Dynamic multi-criteria decision-making (DMCDM) models have many meaningful applications in real life in which solving indeterminacy of information in DMCDMs strengthens the potential application of DMCDM. This study introduces an extension of dynamic internal-valued neutrosophic sets namely generalized dynamic internal-valued neutrosophic sets. Based on this extension, we develop some operators and a TOPSIS method to deal with the change of both criteria, alternatives, and decision-makers by time. In addition, this study also applies the proposal model to a real application that facilitates ranking students according to attitude-skill-knowledge evaluation model. This application not only illustrates the correctness of the proposed model but also introduces its high potential appliance in the education domain.

scholarly journals From Goal Programming for Continuous Multi-Criteria Optimization to the Target Decision Rule for Mixed Uncertain Problems

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 51
Author(s):  
Helena Gaspars-Wieloch
Keyword(s):  
Decision Making ◽  
Decision Rule ◽  
Goal Programming ◽  
Decision Makers ◽  
Decision Making Under Uncertainty ◽  
Multi Criteria Decision Making ◽  
The Novel ◽  
Continuous Version ◽  
Novel Approach

Goal programming (GP) is applied to the discrete and continuous version of multi-criteria optimization. Recently, some essential analogies between multi-criteria decision making under certainty (M-DMC) and scenario-based one-criterion decision making under uncertainty (1-DMU) have been revealed in the literature. The aforementioned similarities allow the adjustment of GP to an entirely new domain. The aim of the paper is to create a new decision rule for mixed uncertain problems on the basis of the GP methodology. The procedure can be used by pessimists, optimists and moderate decision makers. It is designed for one-shot decisions. One of the significant advantages of the novel approach is related to the possibility to analyze neutral criteria, which are not directly taken into account in existing classical procedures developed for 1-DMU.

scholarly journals An Overview of Multi-Criteria Decision-Making Methods in Dealing with Sustainable Energy Development Issues

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2754 ◽  
Author(s):  
Indre Siksnelyte ◽  
Edmundas Zavadskas ◽  
Dalia Streimikiene ◽  
Deepak Sharma
Keyword(s):  
Decision Making ◽  
Swot Analysis ◽  
Sustainable Energy ◽  
Energy Development ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Energy Sustainability ◽  
Widespread Application ◽  
Sustainability Problems ◽  
Scientific Achievements

The measurement of sustainability is actively used today as one of the main preventative instruments in order to reduce the decline of the environment. Sustainable decision-making in solving energy issues can be supported and contradictory effects can be evaluated by scientific achievements of multi-criteria decision-making (MCDM) techniques. The main goal of this paper is to overview the application of decision-making methods in dealing with sustainable energy development issues. In this study, 105 published papers from the Web of Science Core Collection (WSCC) database are selected and reviewed, from 2004 to 2017, related to energy sustainability issues and MCDM methods. All the selected papers were categorized into 9 fields by the application area and into 10 fields by the used method. After the categorization of the scientific articles and detailed analysis, SWOT analysis of MCDM approaches in dealing with sustainable energy development issues is provided. The widespread application and use of MCDM methods confirm that MCDM methods can help decision-makers in solving energy sustainability problems and are highly popular and used in practice.

Some Conflicting Results in the Analytic Hierarchy Process

2019 ◽  
Vol 18 (02) ◽  
pp. 465-486 ◽  
Author(s):  
Ardalan Bafahm ◽  
Minghe Sun
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Decision Makers ◽  
Unexpected Result ◽  
Multi Criteria Decision Making ◽  
Analytic Hierarchy ◽  
Preference Relations ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

The analytic hierarchy process (AHP) has been believed to be one of the most pragmatic and widely accepted methods for multi-criteria decision making. However, there have been various criticisms of this method within the last four decades. In this study, the results of AHP contradicting common expectations are examined for both the distributive and ideal modes. Specifically, conflicting priorities, conflicting decisions, and conflicting preference relations are investigated. A decision-making scenario is used throughout the paper and an illustrative example constructed from the decision-making scenario is provided to demonstrate each of the conflicting results recommended by AHP. With a parametric formulation of each unexpected result, the possibility of unexpected results of AHP is generalized irrespective of applying the distributive or ideal mode. The logic and causes of these contradictions are also analyzed. This study shows that AHP is not always reliable, and could lead the decision makers towards incorrect decisions.

Multi-Criteria Decision-Making Model using Intuitionistic Fuzzy Entropy and Variable Weight Theory

Mekatronika ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 18-25
Author(s):  
Omar Ayasrah ◽  
Faiz Mohd Turan
Keyword(s):  
Decision Making ◽  
Fuzzy Entropy ◽  
Decision Makers ◽  
Entropy Measure ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Variable Weight ◽  
Intuitionistic Fuzzy Entropy ◽  
Perform Sensitivity Analysis ◽  
Almost All

The aim of this research is to develop a new multi-criteria decision-making method that integrates an intuitionistic fuzzy entropy measure and variable weight theory to be implemented in different fields to provide a solution for MCDM problems when the available information is incomplete. A limited number of studies have considered determining decision maker’s weights by performing objective techniques, and almost all of these researches detected a constant weights for the decision makers. In addition, most of the MCDM studies were not formulated to perform sensitivity analysis. The new method is based on the TOPSIS model with an intuitionistic fuzzy entropy measure in the exponential-related function form and the engagement of the variable weight theory to determine weights for the decision-makers that vary as per attibutes. Lastly, a mathematical model was developed in this research to be as an input for developing the mobile-aplication based method in future for virtual use of the new MCDM method.

The Method of Probabilistic Nodes Combination in Decision Making and Risk Analysis

2016 ◽  
pp. 32-60
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Decision Making ◽  
Distribution Function ◽  
Probability Distribution ◽  
Risk Analysis ◽  
Probability Distribution Function ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Characteristic Points ◽  
Basic Probability

Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Nodes can be treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter ? as probability distribution function enables value anticipation in risk analysis and decision making. Two-dimensional curve is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Novelty of the paper consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations.

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